Abramowitch Steven D, Woo Savio L Y, Clineff Theodore D, Debski Richard E
Musculoskeletal Research Center, Department of Orthopaedic Surgery and Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15213, USA.
Ann Biomed Eng. 2004 Mar;32(3):329-35. doi: 10.1023/b:abme.0000017539.85245.6a.
The viscoelastic properties of the healing medial collateral ligament (MCL) at 12 weeks after isolated injury were investigated in a goat model. The stress-strain relationships, static and cyclic stress-relaxation behaviors of the healing MCL up to 5% strain were determined experimentally using a femur-MCL-tibia complex. These experimental data were used in combination with the quasi-linear viscoelastic (QLV) theory of Fung (1972) to characterize the reduced relaxation function, G(t) (described by constants C, tau1, and tau2) and the elastic response, sigmae(epsilon) (described by constants A and B) of this tissue. It was found that the percentage of stress relaxation for the healing MCLs was significantly greater than those for sham-operated controls (49.0 +/- 12.1% vs. 26.5 +/- 8.1%, respectively; p < 0.05). The product of constants A x B, i.e. the initial slope of the stress-strain curves, was found to be significantly lower for healing MCLs compared to those for sham-operated controls (32.9 +/- 15.8 MPa vs. 118.8 +/- 48.3 MPa; p < 0.05). The dimensionless constant C, i.e. the magnitude of the viscous response, was nearly three times greater for healing MCLs, while constant tau1 was found to be similar between the two groups (0.80 +/- 0.43 s vs. 0.89 +/- 0.52 s, respectively). Constant tau2 for the healing MCL was significantly less than the controls (1269 +/- 38 s vs. 1845 +/- 431 s; p < 0.05) indicating that the stress relaxation reached a plateau earlier. These constants of the QLV theory used to describe the healing MCL were validated for the strain level utilized in this experiment (approximately equal to 4.5%) by predicting the peak stresses during a cyclic stress-relaxation experiment. The theoretically determined values closely matched the experimentally measured values. Thus, this study demonstrates that the QLV theory could be successfully used to describe the viscoelastic behavior of the MCL during the early phases of healing.
在山羊模型中，研究了孤立损伤后12周时愈合的内侧副韧带（MCL）的粘弹性特性。使用股骨-MCL-胫骨复合体，通过实验确定了愈合的MCL在高达5%应变时的应力-应变关系、静态和循环应力松弛行为。这些实验数据与冯元桢（1972年）的准线性粘弹性（QLV）理论相结合，以表征该组织的简化松弛函数G(t)（由常数C、τ1和τ2描述）和弹性响应σe(ε)（由常数A和B描述）。结果发现，愈合的MCL的应力松弛百分比显著高于假手术对照组（分别为49.0±12.1%和26.5±8.1%；p<0.05）。发现愈合的MCL的常数A×B的乘积，即应力-应变曲线的初始斜率，与假手术对照组相比显著更低（32.9±15.8兆帕与118.8±48.3兆帕；p<0.05）。无量纲常数C，即粘性响应的大小，愈合的MCL几乎是其近三倍，而发现常数τ1在两组之间相似（分别为0.80±0.43秒和0.89±0.52秒）。愈合的MCL的常数τ2显著小于对照组（1269±38秒与1845±431秒；p<0.05），表明应力松弛更早达到平稳状态。通过预测循环应力松弛实验期间的峰值应力，用于描述愈合的MCL的QLV理论的这些常数在本实验中使用的应变水平（约等于4.5%）下得到了验证。理论确定值与实验测量值紧密匹配。因此，本研究表明QLV理论可成功用于描述愈合早期阶段MCL的粘弹性行为。
